We show that incoherent pumping of an optical lattice clock system with ultracold strontium-88 atoms produces laser light with a ≃10  Hz linewidth when the atoms are exposed to a magnetic field. This linewidth is orders of magnitude smaller than both the cavity linewidth and the incoherent atomic decay and excitation rates. The narrow lasing is due to an interplay of multiatom superradiant effects and the coupling of bright and dark atom-light dressed states by the magnetic field.The nature of level set percolation in the two-dimensional Gaussian free field has been an elusive question. Using a loop-model mapping, we show that there is a nontrivial percolation transition and characterize the critical point. In particular, the correlation length diverges exponentially, and the critical clusters are "logarithmic fractals," whose area scales with the linear size as A∼L^2/sqrt[lnL]. The two-point connectivity also decays as the log of the distance. We corroborate our theory by numerical simulations. Possible conformal field theory interpretations are discussed.We calculate the accurate spectrum of the stochastic gravitational-wave background from U(1) gauge fields produced by axion dark matter. The explosive production of gauge fields soon invalidates the applicability of the linear analysis and one needs nonlinear schemes. We make use of numerical lattice simulations to properly follow the nonlinear dynamics such as backreaction and rescattering which gives important contributions to the emission of gravitational waves. It turns out that the axion with the decay constant f∼10^16  GeV and the mass m∼10^-14  eV which gives the correct dark matter abundance predicts the circularly polarized gravitational-wave signature detectable by SKA. We also show that the resulting gravitational-wave spectrum has a potential to explain NANOGrav 12.5 yr data.The quantum multiparameter estimation is very different from the classical multiparameter estimation due to Heisenberg's uncertainty principle in quantum mechanics. When the optimal measurements for different parameters are incompatible, they cannot be jointly performed. We find a correspondence relationship between the inaccuracy of a measurement for estimating the unknown parameter with the measurement error in the context of measurement uncertainty relations. Taking this correspondence relationship as a bridge, we incorporate Heisenberg's uncertainty principle into quantum multiparameter estimation by giving a trade-off relation between the measurement inaccuracies for estimating different parameters. For pure quantum states, this trade-off relation is tight, so it can reveal the true quantum limits on individual estimation errors in such cases. We apply our approach to derive the trade-off between attainable errors of estimating the real and imaginary parts of a complex signal encoded in coherent states and obtain the joint measurements attaining the trade-off relation. We also show that our approach can be readily used to derive the trade-off between the errors of jointly estimating the phase shift and phase diffusion without explicitly parametrizing quantum measurements.Dissipation generally leads to the decoherence of a quantum state. In contrast, numerous recent proposals have illustrated that dissipation can also be tailored to stabilize many-body entangled quantum states. While the focus of these works has been primarily on engineering the nonequilibrium steady state, we investigate the buildup of entanglement in the quantum trajectories. Specifically, we analyze the competition between two different dissipation channels arising from two incompatible continuous monitoring protocols. The first protocol locks the phase of neighboring sites upon registering a quantum jump, thereby generating a long-range entanglement through the system, while the second destroys the coherence via a dephasing mechanism. By studying the unraveling of stochastic quantum trajectories associated with the continuous monitoring protocols, we present a transition for the scaling of the averaged trajectory entanglement entropies, from critical scaling to area-law behavior. Our work provides an alternative perspective on the measurement-induced phase transition the measurement can be viewed as monitoring and registering quantum jumps, offering an intriguing extension of these phase transitions through the long-established realm of quantum optics.Two-photon interference is a fundamental quantum optics effect with numerous applications in quantum information science. Here, we study two-photon interference in multiple transverse-spatial modes along a single beam-path. Besides implementing the analog of the Hong-Ou-Mandel interference using a two-dimensional spatial-mode splitter, we extend the scheme to observe coalescence and anticoalescence in different three- and four-dimensional spatial-mode multiports. The operation within spatial modes, along a single beam path, lifts the requirement for interferometric stability and opens up new pathways of implementing linear optical networks for complex quantum information tasks.Synthetic gauge fields have recently emerged, arising in the context of quantum simulations, topological matter, and the protected transportation of excitations against defects.  https://www.selleckchem.com/products/dmx-5084.html  For example, an ultracold atom experiences a light-induced effective magnetic field when tunneling in an optical lattice, and offering a platform to simulate the quantum Hall effect and topological insulators. Similarly, the magnetic field associated with photon transport between sites has been demonstrated in a coupled resonator array. Here, we report the first experimental demonstration of a synthetic gauge field in the virtual lattices of bosonic modes in a single optomechanical resonator. By employing degenerate clockwise and counterclockwise optical modes and a mechanical mode, a controllable synthetic gauge field is realized by tuning the phase of the driving lasers. The nonreciprocal conversion between the three modes is realized for different synthetic magnetic fluxes. As a proof-of-principle demonstration, we also show the dynamics of the system under a fast-varying synthetic gauge field, and demonstrate synthetic electric field.